Introduction to 3rd Edition (the mechanics of skill and ability checks)

As characters go up in level, they have the option of improving their current skill set, or adding new ones. Depending on class and race, different types of characters gain skills at different paces. Each skill is based on a numeric skill rank (points you have invested in a skill), an ability modifier appropriate to the skill (dexterity modifier for the balance skill, e.g.) and any racial modifiers. To make a skill check, you roll a d20 and then add the total of your modifiers.

Skills are checked against either a difficulty class (DC) or another opposing skill. For example, to tight rope walk across a 20' chasm, the DM would (possibly) secretly assign a DC (say, 18). Then the character rolls his balance check and gets a 15, adds +5 for his modifiers for a total of 20 - success! Or, a character wants to sneak by an orc guard. He rolls his move silently skill against the orcs hear noise skill, including all bonuses and penalties, the highest roll winning.

Ability checks are similar. For example, to break down a heavy door, the DM could assign a DC of 16. Then the character would have to make a strength check (d20 + strength bonus) and exceed a 16 to break the door.

Taking 10 - If you have a lot of time, and no distractions, you can 'take 10' and get an automatic 10 roll without actually rolling. For example, if swimming across a rushing river is a DC of 12 and you have a +3 str modifier, then taking 10 would give you a 13 and you could swim the river. However, if a band of kobolds starts skipping stones off your head, then you wouldn't be able to take 10 and would have to make the check normally.

Taking 20 - Similar to taking 10, but it takes 20x longer than the action normally would, and the action cannot have any penalty for failure. So, you can't take 20 to climb a wall, because one of those times that you tried, you may fall and take damage. This is also good for searching a room thoroughly. If it would normally take 15 rounds (90 seconds) to search a room, you could take 20 and be sure it was searched in 30 minutes (20 x 90 seconds).

There are also other subtleties to skill checks such as: